4.8 Complex Numbers Learning goals

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Presentation transcript:

4.8 Complex Numbers Learning goals identify, graph, and perform operations with complex numbers find complex number solutions of quadratic equations

Vocabulary complex number: a + bi a is the real number part bi is the imaginary number part If b is 0, then a is a real number; if a is 0, then bi is a pure imaginary number

imaginary number (i)

Ex 1

Ex 2 Write in a + bi form

Ex 3

Ex 4

Imaginary numbers pattern MEMORIZE!!!!!!

Ex 5

Ex 6 Solve

Complex Conjugates Complex conjugates are used to rationalize complex binomials found in the denominator The product of complex conjugates is a REAL number Why can’t there be an i in the denominator of a fraction?

Ex 7 Simplify

Ex 8 Simplify

Think about it… Explain the difference between the additive inverse of a complex number and complex conjugate.